Theoretical studies of sea animal locomotion, Part 1

Conclusion

This paper tries to apply methods of aerofoil theory in two-dimensional, nonsteady flow of incompressible fluids to a mathematical model simulating fish locomotion. The theoretical results for the thrust coefficients are found to be in good agreement with the experimental data measured by A. W. Rentz of NOTS in the CIT Free Surface Water Tunnel. There are, however, two domains which deserve special attention: the ranges of high and low frequencies. At high frequencies nonlinear effects become important so that the linearized theory fails to give a satisfactory answer. Also a noticeable deviation between the theoretical curves and experimental values is observed at very low frequencies. Although viscosity has been neglected in this analysis, we know that there is a considerable contribution of skin friction to drag. Therefore, it is understood that the behavior of the boundary layer plays an essential role, especially in the low frequency range, where the indicated drag is much greater than would be predicted for steady flow, even with a turbulent boundary layer.

Investigations concerning boundary layer theory and extensions of the present theory to two-dimensional thick profiles and three-dimensional slender fish-like bodies will be communicated later.

The equipment was designed and built by G. H. Bowlus of NOTS. A separate report dealing with the experimental part of the project is to appear.